1. A Survey on Graph Visualization 1 Presented by Yang Zhang Dave Fuhry

2. Challenges 2 Graph Layout – Make a concrete rendering of graph. Scale for large graphs – Render on a computer screen with limited pixels – High computational cost Interaction – Show more detail for area of interest – Exploration for intuition

3. Force-Directed Layout Nodes are modeled as physical bodies that are connected through springs (edges) – Pseudo code Pseudo code – Example Example High running time – The typical force-directed algorithms are in general considered to have a running time equivalent to O(n 3 ), where n is the number of nodes of the input graph. 3

4. Pseudo Code 4 set up initial node positions randomly loop total_kinetic_energy := 0 for each node net-force := (0, 0) for each other node net-force := net-force + repulsion( this_node, other_node ) for each spring connected to this node net-force := net-force + attraction( this_node, spring ) // without damping, it moves forever this_node.velocity := (this_node.velocity + timestep * net- force) * damping this_node.position := this_node.position + timestep * this_node.velocity total_kinetic_energy := total_kinetic_energy + this_node.mass *(this_node.velocity)^2 until total_kinetic_energy is less than some small number // the simulation has stopped moving

5. Zoom and pan Zoom for graphs exact, adjustment of screen transformations The internet map: http://internet-map.net/http://internet-map.net/

6. Hierarchical Clustering Successively applying the clustering process to clusters discovered by a previous step. Can be navigated as tree

7. Example: ASK-GraphView 7

8. Dynamic Graphs Events in dynamic graphs

9. Event-View Interface 9

10. Event Visualization 10

11. Visualizing Cohesive Subgraphs cohesive subgraphs – A subgraph in which vertices are densely connected. – Clique, K-Core, etc. CSV – For each edge e, compute c(e), which is the size of the biggest clique that contains e. – Plot each vertex in the following order: Randomly pick up the first vertex to plot; Pick up the next vertex which shares an edge with maximum c(e) with previously plotted vertices. Plot the vertex with height = c(e) – The peaks indicate dense cohesive subgraphs 11

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13. Directed K-Core : D-core D = (V;E) is a digraph that is a set V of vertices and a set E of directed edges between them. The min-in-degree and the min-out-degree of a digraph D are defined as a (k; l)-D-core of D is a maximal sub-digraph F of D where Denoted as

14. D-core matrix For directed graph D, there is a unique (k; l)-D-core for each (k; l). We define D-core matrix AD as follows: AD(k; l) = size of (k; l)-D-core.

15. Tools Web-based tools Cobweb: http://bioinformatics.charite.de/cobweb/http://bioinformatics.charite.de/cobweb/ Sigma.js: http://sigmajs.org/http://sigmajs.org/ InfoVis: http://thejit.org/http://thejit.org/ Cytoscape web: http://cytoscapeweb.cytoscape.org/http://cytoscapeweb.cytoscape.org/ Applications Gephi: http://gephi.org/http://gephi.org/ Cytoscape: http://www.cytoscape.org/http://www.cytoscape.org/ Guess: http://graphexploration.cond.org/index.htmlhttp://graphexploration.cond.org/index.html 15